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Q.
Current provided by a battery is maximum when:
AFMCAFMC 2004Current Electricity
Solution:
Let $n$ cells are connected in series, and such $m$ series are connected in parallel. Let the emf of each cell be $E$ and the internal resistance be $r$.This battery of cells is sending current in an external resistance $R$. Then current in the external circuit be $i$, then $i=\frac{m n E}{n r+m R}$
It is clear from this equation, that for current to be maximum the value of $(n r+m R)$ should be minimum.
i.e., $n r+m R=[\sqrt{n r}-\sqrt{m R}]^{2}+2 \sqrt{m n R r}$
It's minimum value is zero.
i.e., $[\sqrt{n r}-\sqrt{m R}]^{2}=0$
$\sqrt{n r}-\sqrt{m R}=0$
$n r=m R$
$R=\frac{n r}{m}$
but $\frac{n r}{m}$ is the internal resistance of the whole battery. Thus, current is maximum when the internal resistance of battery is equal to external resistance.
